Depending on your iPod nano generation, the correct button may be in a different position. If you have the latest iPod nano with a touch screen without a click wheel on the front, the Sleep/Wake button is located on the top of your device. Press and hold this button until you see the Apple logo. To turn on your iPod nano (older) with a click wheel on the front, press any button on the front until you see the Apple logo.
If your iPod is not turning on after a few seconds, the battery is probably drained. Charge the battery. In this case, connect the iPod to a wall outlet using the cable that came with it.